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Physics

Fluid-Mechanics

Easy

Question

A cylinder containing water upto a height of 25 cm has a hole of cross section $1 fourth c m squared$ at its bottom. It is counter passed in a balance. When water begins to flow out, the initial change in the balancing weight is

Increase of 12.5 gm wt
Increase of 6.25 gm wt
Decrease of 12.5 gm wt
Decrease of 6.25 gm wt

The correct answer is: Decrease of 12.5 gm wt

Let v be the initial velocity of efflux of water.
Initial volume of water flowing out per sec = av
Initial mass of the water flowing out per sec $equals a v d equals a v cross times 1 equals a v$
Rate of change of momentum $equals left parenthesis a v right parenthesis v equals a v squared$
Initial downward force on the out flowing water = av²
Reaction acts upwards on the cylinder
Initial upward reaction = av²
Initial decrease in weight $equals a cross times 2 g h equals 1 fourth cross times 2 cross times g cross times 25 equals 12 times 5 cross times g equals 12 times 5 g m minus w t$

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